On the asymptotic properties of the Hessian in discrete-time linear quadratic control

This paper studies the asymptotic properties of the Hessian in discrete-time linear quadratic optimal control. We show that the singular values of the Hessian converge, in a well defined sense, to the principal gains in the frequency domain of an associated normalized system transfer function. We treat the stable and unstable case for multi-input multi-output linear systems. Potential applications of the ideas presented here include fast and/or robust algorithms for constrained model predictive control of discrete-time linear systems.